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International Conference on Typed Lambda Calculi and Applications

TLCA 1999: Typed Lambda Calculi and Applications pp 280–294Cite as

A Curry-Howard Isomorphism for Compilation and Program Execution

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1581))

Abstract

This paper establishes a Curry-Howard isomorphism for compilation and program execution by showing the following facts. (1) The set of A-normal forms, which is often used as an intermediate language for compilation, corresponds to a subsystem of Kleene’s contraction-free variant of Gentzen’s intuitionistic sequent calculus. (2) Compiling the lambda terms to the set of A-normal forms corresponds to proof transformation from the natural deduction to the sequent calculus followed by proof normalization. (3) Execution of an A-normal form corresponds to a special proof reduction in the sequent calculus. Different from cut elimination, this process eliminates left rules by converting them to cuts of proofs corresponding to closed values. The evaluation of an entire program is the process of inductively applying this process followed by constructing data structures.

This work was partly supported by the Japanese Ministry of Education Grant-in-Aid for Scientific Research on Priority Area no. 275 “Advanced databases,” and by the Parallel and Distributed Processing Research Consortium, Japan.

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Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-8502, Japan

    Atsushi Ohori

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  1. Atsushi Ohori
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Editors and Affiliations

  1. CNRS - UPR9016, Institut de Mathématiques de Luminy, 163 Avenue de Luminy, case 907, F-13288, Marseille cedex 9, France

    Jean-Yves Girard

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© 1999 Springer-Verlag Berlin Heidelberg

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Ohori, A. (1999). A Curry-Howard Isomorphism for Compilation and Program Execution. In: Girard, JY. (eds) Typed Lambda Calculi and Applications. TLCA 1999. Lecture Notes in Computer Science, vol 1581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48959-2_20

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  • DOI: https://doi.org/10.1007/3-540-48959-2_20

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-65763-7

  • Online ISBN: 978-3-540-48959-7

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